Chaitin's Constant

He even did more:<p>Mathematician GregoryChaitin defines elegance in computer programming in this way: A computer program written in a given language is elegant if no smaller program written in the same language has the same output. He goes on to prove that it is impossible to prove that a given program above a certain very low level of complexity is elegant.<p><a href="https:&#x2F;&#x2F;wiki.c2.com&#x2F;?ChaitinElegance" rel="nofollow">https:&#x2F;&#x2F;wiki.c2.com&#x2F;?ChaitinElegance</a><p>And he gave some examples in his book.<p><a href="http:&#x2F;&#x2F;jillian.rootaction.net&#x2F;~jillian&#x2F;science&#x2F;chaitin&#x2F;www.cs.umaine.edu&#x2F;chaitin&#x2F;unknowable&#x2F;index.html" rel="nofollow">http:&#x2F;&#x2F;jillian.rootaction.net&#x2F;~jillian&#x2F;science&#x2F;chaitin&#x2F;www.c...</a><p>See the example code in LISP here:<p><a href="https:&#x2F;&#x2F;github.com&#x2F;darobin&#x2F;chaitin-lisp" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;darobin&#x2F;chaitin-lisp</a>

If you want to read a bit more from the mathematician himself on this very topic he wrote an accessible &quot;pop-math&quot; book about it, &quot;Meta Math!: The Quest for Omega&quot; though you&#x27;ll need to look beyond the author&#x27;s rather strange choices of metaphor (<a href="https:&#x2F;&#x2F;www.goodreads.com&#x2F;book&#x2F;show&#x2F;249849.Meta_Math_" rel="nofollow">https:&#x2F;&#x2F;www.goodreads.com&#x2F;book&#x2F;show&#x2F;249849.Meta_Math_</a>).

I just want to drop this playlist here <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=HLPO-RTFU2o&amp;list=PL86ECDEDE3FA8D8D1" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=HLPO-RTFU2o&amp;list=PL86ECDEDE3...</a> as its one of my fav lectures<p>Gregory Chaitin Lecture at Carnegie-Mellon University in 2000, he gives a bit of history of parts of math&#x2F;computing that leads up to him talking about qualities of random. He touches on Cantor, Bertrand Russell, Hilbert, Gödel and Turing.

Afaict Chaitin independently came up with the concept of Kolmogorov complexity... as a teenager!

The surprising thing to me was, following the link to &quot;normal numbers&quot;, that this is called out as one of the only proved irrational normal numbers, even though it is proven that the set of irrational numbers is normal almost everywhere.

Can somebody explain to me how is this useful? Is it used for anything?<p>Or is it pure theoretical concept with interesting emerging properties.

Numberphile has a video explaining the relationship between the number categories, and includes a brief discussion of where Chaitin&#x27;s Constant belongs.<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=5TkIe60y2GI" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=5TkIe60y2GI</a>

In contrast: <a href="https:&#x2F;&#x2F;www.jamesrmeyer.com&#x2F;topics&#x2F;chaitins-omega.html" rel="nofollow">https:&#x2F;&#x2F;www.jamesrmeyer.com&#x2F;topics&#x2F;chaitins-omega.html</a>

I&#x27;m a fan of Fulton&#x27;s constant.<p>Fulton&#x27;s constant is any number of 9s. E.g., 9, 999, or 999999.

Not to be confused with his Croissant.